Document Type : Research Paper


1 Department of Industrial and Systems Engineering, Isfahan University of Technology

2 Department of Industrial and Systems Engineering, Isfahan University of Technology,

3 Department of Industrial Engineering, University of Louisville, KY, USA

4 Guildhall School of Business and Law, London Metropolitan University, United Kingdom

5 Department of Ocean Operations and Civil Engineering, Faculty of Engineering, NTNU Ålesund, Ålesund, Norway.



The objective of this study is to model a dynamic redesigning closed-loop supply chain network with capacity planning in order to minimize the costs of the network. The structure of this model consists of existing facilities including manufacturing plants, distribution and reworking centers. Any such structure should change due to fluctuations in demand in order to meet customer demand. Establishing new facilities, closing the existing ones, and adding discrete capacity levels to facilities, are among the decisions which lead to necessary changes in network structure. To make the issue more realistic, it is assumed that demand and returned products are stochastic. To solve the problem, a two-stage stochastic mixed integer linear programming is modelled, followed by writing a robust counterpart of the MILP model program. An accelerated Benders decomposition algorithm is proposed to solve this model. To increase the convergence trend of this proposed algorithm, valid-inequalities and Pareto optimal cut are combined to the model. The expected performance improvement based on applying valid-inequalities and Pareto optimal cut is expressed through numerical results obtained from different samples.


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